My son is 7 month old. He has persistent cough from last 3 months. Doctors are giving antibiotics and expectorant to him but still cough persists.?

Further evaluation. First, if there is no indication for antibiotics, they need to be stopped. Cough could be several things, including asthma, reflux, etc. You may need to see someone else if you aren't getting anywhere. A pediatric pulmonologist may be a good way to go.
Allergies possible. Lots of things cause cough in infants, such as allergies/asthma and reflux. An allergist can help sort this out.